The cartesian two-dimensional point. More...

#include <mb_cart_point.h>

Collaboration diagram for MbCartPoint:

Public Member Functions
	MbCartPoint ()
	Default constructor. More...

	MbCartPoint (const MbCartPoint &p)
	Copy-constructor.

	MbCartPoint (const MbVector &p)
	Constructor by a vector.

	MbCartPoint (double initX, double initY)
	Constructor by coordinates.

	MbCartPoint (const MbCartPoint &p, const MbMatrix &matr)
	Constructor by a point in a local coordinate system. More...

	MbCartPoint (const MbFloatPoint &)
	Constructor by float point.

void	SetZero ()
	Set coordinates to zero.

template<class Point >
MbCartPoint &	Init (const Point &p)
	Initialize by another point.

MbCartPoint &	Init (double initX, double initY)
	Initialize by coordinates.

double	DistanceToPoint (const MbCartPoint &to) const
	Find the distance between points.

MbCartPoint &	Transform (const MbMatrix &matr)
	Transform according to the matrix.

MbCartPoint &	Move (const MbVector &to)
	Translate along a vector.

MbCartPoint &	Move (double dx, double dy)
	Translate by given increments.

double	DistanceToPoint2 (const MbCartPoint &to) const
	Find the squared distance between points.

double	DistanceToLineSeg (const MbCartPoint &p1, const MbCartPoint &p2, double eps=Math::LengthEps) const
	The distance from a point to a segment. More...

double	Length () const
	The vector length ( 0, p(x,y) ).

void	Scale (double sx, double sy)
	Scale the coordinates. More...

void	GetProperties (MbProperties &properties)
	Get properties of the object.

void	SetProperties (const MbProperties &properties)
	Set properties of the object.

bool	IsSame (const MbCartPoint &other, double accuracy) const
	Are the objects equal? More...

bool	IsUndefined () const
	Is the point undefined?

Translations, rotations, reflections.
void	MoveAlongLine (const MbCartPoint &p2, double delta)
	Translate along the direction which is defined by a second point. More...

void	MoveAlongLine (double angle, double delta)
	Translate along the direction which is defined by an angle. More...

void	MoveAlongLine (const MbDirection &angle, double delta)
	Translate along the direction which is defined by a vector. More...

void	MoveAlongLine (const MbVector &vect, double delta)
	Translate along the direction which is defined by a vector. More...

void	MoveUntilDist (const MbCartPoint &p1, double dist)
	Translate the point towards a given point to the distance "dist". More...

void	GoNearToPoint (const MbCartPoint &to, double ratio)
	Translate along the direction. More...

void	Rotate (const MbCartPoint &pnt, double angle)
	Rotate by an angle. More...

void	Rotate (const MbCartPoint &pnt, const MbDirection &angle)
	Rotate by an angle. More...

void	Rotate (double angle)
	Rotate by an angle. More...

void	Rotate (const MbDirection &angle)
	Rotate by an angle. More...

MbCartPoint	Mirror (const MbCartPoint &from) const
	Reflect a point specularly from a given point. More...

MbCartPoint	Mirror (const MbCartPoint &p1, const MbCartPoint &p2) const
	Reflect a point specularly from a line. More...

void	Mirror (const MbCartPoint &p1, const MbDirection &dir)
	Reflect a point specularly from a line. More...

Logical and arithmetical operations.
double &	operator[] (size_t i)
	Access to a coordinate by an index.

double	operator[] (size_t i) const
	The value of a coordinate by an index.

bool	operator== (const MbCartPoint &with) const
	Check for equality with tolerance.

bool	operator!= (const MbCartPoint &with) const
	Check for inequality.

bool	Equal (const MbCartPoint &with) const
	Check for an accurate equality.

bool	operator< (const MbCartPoint &) const
	Check for "less".

bool	operator> (const MbCartPoint &) const
	Check for "greater".

MbVector	operator+ (const MbCartPoint &pnt) const
	Sum two points.

MbVector	operator- (const MbCartPoint &pnt) const
	Subtract a point from the point.

MbCartPoint	operator+ (const MbDirection &d) const
	Add a point to a vector.

MbCartPoint	operator- (const MbDirection &d) const
	Subtract a vector from a point.

MbCartPoint	operator- () const
	The unary minus.

MbCartPoint	operator* (double factor) const
	Multiply a point by a number.

MbCartPoint	operator/ (double factor) const
	Divide a point by a number.

MbCartPoint	operator* (const MbMatrix &) const
	Calculate the point as this copy transformed by the matrix.

void	operator+= (const MbCartPoint &pnt)
	Sum two points.

void	operator-= (const MbCartPoint &pnt)
	Subtract a point from the point.

void	operator*= (double factor)
	Multiply a point by a number.

void	operator/= (double factor)
	Divide a point by a number.

void	operator+= (MbVector &v)
	Add a point to a vector.

void	operator-= (MbVector &v)
	Subtract a vector from a point.

MbCartPoint	operator+ (const MbVector &vector) const
	Add a point to a vector.

MbCartPoint	operator- (const MbVector &vector) const
	Subtract a vector from a point.

MbCartPoint &	operator= (const MbCartPoint &)
	Assign the value of another point to the point.

void	operator= (const MbVector &)
	Assign values of vector components to the point.

void	operator= (const MbDirection &)
	Assign values of vector components to the point.

void	operator= (const MbFloatPoint &)
	Assign the float-point value to the point.

The functions of addition and multiplication of points with points and vectors.
void	Set (const MbCartPoint &v1, const MbVector &v2, double t2)
	Equate coordinates to sum of point coordinates and vector coordinates. More...

void	Set (const MbCartPoint &v1, const MbVector &v2, double t2, const MbVector &v3, double t3)
	Equate coordinates to sum of point coordinates and two vectors coordinates. More...

void	Set (const MbCartPoint &v1, double t1, const MbCartPoint &v2, double t2)
	Equate coordinates to sum of two points coordinates. More...

void	Set (const MbCartPoint &v1, double t1, const MbCartPoint &v2, double t2, const MbCartPoint &v3, double t3)
	Equate coordinates to sum of three points coordinates. More...

void	Set (const MbCartPoint &v1, double t1, const MbCartPoint &v2, double t2, const MbCartPoint &v3, double t3, const MbCartPoint &v4, double t4)
	Equate coordinates to sum of four points coordinates. More...

void	Set (const MbCartPoint &v1, const MbDirection &v2, double t2, const MbDirection &v3, double t3)
	Equate coordinates to sum of point coordinates and two vectors coordinates. More...

void	Add (const MbVector &v1, double t1)
	Increase coordinates by values of vector components. More...

void	Add (const MbVector &v1, double t1, const MbVector &v2, double t2)
	Increase coordinates by values of two vectors components. More...

void	Add (const MbVector &v1, double t1, const MbVector &v2, double t2, const MbVector &v3, double t3)
	Increase coordinates by values of v1, v2 and v3 vectors components multiplied by t1, t2 and t3 respectively. More...

void	Add (const MbVector &v1, double t1, const MbVector &v2, double t2, const MbVector &v3, double t3, const MbVector &v4, double t4)
	Increase coordinates by values of three vectors components. More...

void	Add (const MbDirection &v1, double t1, const MbDirection &v2, double t2)
	Increase coordinates by values of two vectors components. More...

void	Add (const MbCartPoint &v1, double t1)
	Increase coordinates by values of point coordinates. More...

void	Add (const MbCartPoint &v1, double t1, const MbCartPoint &v2, double t2, const MbCartPoint &v3, double t3)
	Increase coordinates by values of three points coordinates. More...

void	Add (const MbCartPoint &v1, double t1, const MbCartPoint &v2, double t2, const MbCartPoint &v3, double t3, const MbCartPoint &v4, double t4)
	Increase coordinates by values of four points coordinates. More...

Static Public Member Functions
static size_t	GetDimension ()
	The number of point coordinates.

Public Attributes
double	x
	A first coordinate of point.

double	y
	A second coordinate of point.

Static Public Attributes
static const MbCartPoint	origin
	The origin or { 0, 0 }.

Detailed Description

The cartesian two-dimensional point.

The two-dimensional point is defined by two coordinates. Different logical, arithmetical and geometrical operations of points with points and vectors are defined. The point is named in honor of French scientist Rene Descartes (lat. Renatus Cartesius).

Constructor & Destructor Documentation

◆ MbCartPoint() [1/2]

MbCartPoint::MbCartPoint ( )

inline

Default constructor.

Creates a point with zero coordinates.

◆ MbCartPoint() [2/2]

MbCartPoint::MbCartPoint	(	const MbCartPoint &	p,
		const MbMatrix &	matr
	)

inline

Constructor by a point in a local coordinate system.

A transition matrix is given for transforming of a point to the global coordinate system from a local coordinate system.

Parameters

[in]	p	- A point in the local coordinate system.
[in]	matr	- A transition matrix from the local coordinate system to the global coordinate system.

Member Function Documentation

◆ MoveAlongLine() [1/4]

void MbCartPoint::MoveAlongLine	(	const MbCartPoint &	p2,
		double	delta
	)

Translate along the direction which is defined by a second point.

Parameters

[in]	p2	- An initial point, which defines the direction of the translation.
[in]	delta	- Magnitude of the translation.

◆ MoveAlongLine() [2/4]

void MbCartPoint::MoveAlongLine	(	double	angle,
		double	delta
	)

inline

Translate along the direction which is defined by an angle.

Parameters

[in]	angle	- An angle which defines the direction of the translation.
[in]	delta	- Magnitude of the translation.

◆ MoveAlongLine() [3/4]

void MbCartPoint::MoveAlongLine	(	const MbDirection &	angle,
		double	delta
	)

inline

Translate along the direction which is defined by a vector.

Parameters

[in]	angle	- A vector which defines the direction of the translation.
[in]	delta	- Magnitude of the translation.

◆ MoveAlongLine() [4/4]

void MbCartPoint::MoveAlongLine	(	const MbVector &	vect,
		double	delta
	)

inline

Translate along the direction which is defined by a vector.

Parameters

[in]	angle	- A vector which defines the direction of the translation.
[in]	delta	- Magnitude of the translation.

◆ MoveUntilDist()

void MbCartPoint::MoveUntilDist	(	const MbCartPoint &	p1,
		double	dist
	)

Translate the point towards a given point to the distance "dist".

Parameters

[in]	p1	- An initial point, which defines the direction of the translation.
[in]	dist	- Magnitude of the translation.

◆ GoNearToPoint()

void MbCartPoint::GoNearToPoint	(	const MbCartPoint &	to,
		double	ratio
	)

inline

Translate along the direction.

Translation along the direction of the "to" point to the distance which is defined by the ratio of "ratio" and distance between points.

Parameters

[in]	to	- A point.
[in]	ratio	- A distance part.

◆ Rotate() [1/4]

void MbCartPoint::Rotate	(	const MbCartPoint &	pnt,
		double	angle
	)

inline

Rotate by an angle.

An angle defines a rotation vector and a point defines a center.

Parameters

[in]	pnt	- A point.
[in]	angle	- A rotation angle.

◆ Rotate() [2/4]

void MbCartPoint::Rotate	(	const MbCartPoint &	pnt,
		const MbDirection &	angle
	)

Rotate by an angle.

An angle is defined by a rotation vector.

Parameters

[in]	pnt	- A point is a rotation center.
[in]	angle	- A rotation vector.

◆ Rotate() [3/4]

void MbCartPoint::Rotate ( double angle )

inline

Rotate by an angle.

An angle defines a rotation vector.

Parameters

[in] angle - A rotation angle.

◆ Rotate() [4/4]

void MbCartPoint::Rotate ( const MbDirection & angle )

Rotate by an angle.

An angle is defined by a rotation vector.

Parameters

[in] angle - A rotation vector.

◆ Mirror() [1/3]

MbCartPoint MbCartPoint::Mirror ( const MbCartPoint & from ) const

inline

Reflect a point specularly from a given point.

Parameters

[in] from - A point from which it is necessary to reflect the initial point.

Returns: Returns a reflected point.

◆ Mirror() [2/3]

MbCartPoint MbCartPoint::Mirror	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2
	)		const

Reflect a point specularly from a line.

Parameters

[in] p1,p2 - Points which define a line.

Returns: Returns a reflected point.

◆ Mirror() [3/3]

void MbCartPoint::Mirror	(	const MbCartPoint &	p1,
		const MbDirection &	dir
	)

inline

Reflect a point specularly from a line.

The reflection from a line in the direction which is defined by the base point.

Parameters

[in]	p1	- A point which defines the direction of the reflection.
[in]	dir	- A vector defines a line from which the reflection is made.

◆ DistanceToLineSeg()

double MbCartPoint::DistanceToLineSeg	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		double	eps = `Math::LengthEps`
	)		const

The distance from a point to a segment.

A segment is defined by two input points,

Parameters

[in] p1,p2 - Start and end points of a segment.

Returns: The required distance.

◆ Scale()

void MbCartPoint::Scale	(	double	sx,
		double	sy
	)

inline

Scale the coordinates.

Parameters

[in] sx,sy - Scaling coefficients for components x & y respectively.

◆ Set() [1/6]

void MbCartPoint::Set	(	const MbCartPoint &	v1,
		const MbVector &	v2,
		double	t2
	)

inline

Equate coordinates to sum of point coordinates and vector coordinates.

Equate coordinates to sum of v1 point coordinates and v2 vector coordinates multiplied by t2.

Parameters

[in]	v1	- The initial point.
[in]	v2	- The initial vector.
[in]	t2	- Coordinates of the initial vector v2 are multiplied by this number.

◆ Set() [2/6]

void MbCartPoint::Set	(	const MbCartPoint &	v1,
		const MbVector &	v2,
		double	t2,
		const MbVector &	v3,
		double	t3
	)

inline

Equate coordinates to sum of point coordinates and two vectors coordinates.

Equate coordinates to sum of v1 point coordinates and v2 and v3 vectors coordinates multiplied by the numbers t2 and t3 respectively.

Parameters

[in]	v1	- The initial point.
[in]	v2,v3	- The initial vectors.
[in]	t2,t3	- Coordinates of v2 and v3 vectors are multiplied by these numbers respectively.

◆ Set() [3/6]

void MbCartPoint::Set	(	const MbCartPoint &	v1,
		double	t1,
		const MbCartPoint &	v2,
		double	t2
	)

inline

Equate coordinates to sum of two points coordinates.

Equate coordinates to sum of v1 and v2 points coordinates multiplied by the numbers t1 and t2 respectively.

Parameters

[in]	v1,v2	- Initial points.
[in]	t1,t2	- Coordinates of v1 and v2 points are multiplied by these numbers respectively.

◆ Set() [4/6]

void MbCartPoint::Set	(	const MbCartPoint &	v1,
		double	t1,
		const MbCartPoint &	v2,
		double	t2,
		const MbCartPoint &	v3,
		double	t3
	)

inline

Equate coordinates to sum of three points coordinates.

Equate coordinates to sum of v1, v2 and v3 points coordinates multiplied by the numbers t1, t2 and t3 respectively.

Parameters

[in]	v1,v2,v3	- Initial points.
[in]	t1,t2,t3	- Coordinates of v1, v2 and v3 points are multiplied by these numbers respectively.

◆ Set() [5/6]

void MbCartPoint::Set	(	const MbCartPoint &	v1,
		double	t1,
		const MbCartPoint &	v2,
		double	t2,
		const MbCartPoint &	v3,
		double	t3,
		const MbCartPoint &	v4,
		double	t4
	)

inline

Equate coordinates to sum of four points coordinates.

Equate coordinates to sum of v1, v2, v3 and v4 points coordinates multiplied by the numbers t1, t2, t3 and t4 respectively.

Parameters

[in]	v1,v2,v3,v4	- Initial points.
[in]	t1,t2,t3,t4	- Coordinates of v1, v2, v3 and v4 points are multiplied by these numbers respectively.

◆ Set() [6/6]

void MbCartPoint::Set	(	const MbCartPoint &	v1,
		const MbDirection &	v2,
		double	t2,
		const MbDirection &	v3,
		double	t3
	)

inline

Equate coordinates to sum of point coordinates and two vectors coordinates.

Equate coordinates to sum of v1 point coordinates and v2 and v3 vectors coordinates multiplied by the numbers t2 and t3 respectively.

Parameters

[in]	v1	- The initial point.
[in]	v2,v3	- The initial vectors.
[in]	t2,t3	- Coordinates of v2 and v3 vectors are multiplied by these numbers respectively.

◆ Add() [1/8]

void MbCartPoint::Add	(	const MbVector &	v1,
		double	t1
	)

inline

Increase coordinates by values of vector components.

Increase coordinates by values of v1 vector components multiplied by t1.

Parameters

[in]	v1	- The initial vector.
[in]	t1	- Coordinates of the initial vector v1 are multiplied by this number.

◆ Add() [2/8]

void MbCartPoint::Add	(	const MbVector &	v1,
		double	t1,
		const MbVector &	v2,
		double	t2
	)

inline

Increase coordinates by values of two vectors components.

Increase coordinates by values of v1 and v2 vectors components multiplied by the numbers t1 and t2 respectively.

Parameters

[in]	v1,v2	- The initial vectors.
[in]	t1,t2	- Coordinates of v1 and v2 vectors are multiplied by these numbers respectively.

◆ Add() [3/8]

void MbCartPoint::Add	(	const MbVector &	v1,
		double	t1,
		const MbVector &	v2,
		double	t2,
		const MbVector &	v3,
		double	t3
	)

inline

Increase coordinates by values of v1, v2 and v3 vectors components multiplied by t1, t2 and t3 respectively.

Parameters

[in]	v1,v2,v3	- The initial vectors.
[in]	t1,t2,t3	- Coordinates of v1, v2 and v3 vectors are multiplied by these numbers respectively.

◆ Add() [4/8]

void MbCartPoint::Add	(	const MbVector &	v1,
		double	t1,
		const MbVector &	v2,
		double	t2,
		const MbVector &	v3,
		double	t3,
		const MbVector &	v4,
		double	t4
	)

inline

Increase coordinates by values of three vectors components.

Increase coordinates by values of v1, v2 and v3 vectors components multiplied by the numbers t1, t2 and t3 respectively.

Parameters

[in]	v1,v2,v3	- The initial vectors.
[in]	t1,t2,t3	- Coordinates of v1, v2 and v3 vectors are multiplied by these numbers respectively.

◆ Add() [5/8]

void MbCartPoint::Add	(	const MbDirection &	v1,
		double	t1,
		const MbDirection &	v2,
		double	t2
	)

inline

Increase coordinates by values of two vectors components.

Increase coordinates by values of v1 and v2 vectors components multiplied by the numbers t1 and t2 respectively.

Parameters

[in]	v1,v2	- The initial vectors.
[in]	t1,t2	- Coordinates of v1 and v2 vectors are multiplied by these numbers respectively.

◆ Add() [6/8]

void MbCartPoint::Add	(	const MbCartPoint &	v1,
		double	t1
	)

inline

Increase coordinates by values of point coordinates.

Increase coordinates by values of v1 point coordinates multiplied by t1.

Parameters

[in]	v1	- The initial point.
[in]	t1	- Coordinates of the initial point v1 are multiplied by this number.

◆ Add() [7/8]

void MbCartPoint::Add	(	const MbCartPoint &	v1,
		double	t1,
		const MbCartPoint &	v2,
		double	t2,
		const MbCartPoint &	v3,
		double	t3
	)

inline

Increase coordinates by values of three points coordinates.

Increase coordinates by values of v1, v2 and v3 points coordinates multiplied by the numbers t1, t2 and t3 respectively.

Parameters

[in]	v1,v2,v3	- Initial points.
[in]	t1,t2,t3	- Coordinates of v1, v2 and v3 points are multiplied by these numbers respectively.

◆ Add() [8/8]

void MbCartPoint::Add	(	const MbCartPoint &	v1,
		double	t1,
		const MbCartPoint &	v2,
		double	t2,
		const MbCartPoint &	v3,
		double	t3,
		const MbCartPoint &	v4,
		double	t4
	)

inline

Increase coordinates by values of four points coordinates.

Increase coordinates by values of v1, v2, v3 and v4 points coordinates multiplied by the numbers t1, t2, t3 and t4 respectively.

Parameters

[in]	v1,v2,v3,v4	- Initial points.
[in]	t1,t2,t3,t4	- Coordinates of v1, v2, v3 and v4 points are multiplied by these numbers respectively.

◆ IsSame()

bool MbCartPoint::IsSame	(	const MbCartPoint &	other,
		double	accuracy
	)		const

inline

Are the objects equal?

The objects are equal if their data are equal with a given accuracy.

Parameters

[in]	other	- The object to compare.
[in]	accuracy	- The accuracy to compare.

Returns: Whether the objects are equal.

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MbCartPoint() [1/2]

◆ MbCartPoint() [2/2]

Member Function Documentation

◆ MoveAlongLine() [1/4]

◆ MoveAlongLine() [2/4]

◆ MoveAlongLine() [3/4]

◆ MoveAlongLine() [4/4]

◆ MoveUntilDist()

◆ GoNearToPoint()

◆ Rotate() [1/4]

◆ Rotate() [2/4]

◆ Rotate() [3/4]

◆ Rotate() [4/4]

◆ Mirror() [1/3]

◆ Mirror() [2/3]

◆ Mirror() [3/3]

◆ DistanceToLineSeg()

◆ Scale()

◆ Set() [1/6]

◆ Set() [2/6]

◆ Set() [3/6]

◆ Set() [4/6]

◆ Set() [5/6]

◆ Set() [6/6]

◆ Add() [1/8]

◆ Add() [2/8]

◆ Add() [3/8]

◆ Add() [4/8]

◆ Add() [5/8]

◆ Add() [6/8]

◆ Add() [7/8]

◆ Add() [8/8]

◆ IsSame()